how many miles on car? squealing noise is probably belt, is it constant or does it ever stop squealing? to test if it is belt take some liquid soap in a squirt bottle and spray a little on the inside of the belt grooves and let the car run a while if it is a belt it will quieten down. if it gets quiet you will probably need to change the belt., has the fuel filter ever been changed and the air filter?how many miles on car? squealing noise is probably belt, is it constant or does it ever stop squealing? to test if it is belt take some liquid soap in a squirt bottle and spray a little on the inside of the belt grooves and let the car run a while if it is a belt it will quieten down. if it gets quiet you will probably need to change the belt., has the fuel filter ever been changed and the air filter?

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sounds like you need to replace the power steering pump,of not overheating or loosing coolant,would check water pump,if no power steering sonds like the pump is bad,mechanic depepnding on their ability could change for you,up to you if you want to pay a shop to replace pump.

Sounds like you have a loose belt. A cold belt is stiff and slippery, but gets softer and more tacky when it is warm. The belt may either be worn, or just loose. If just loose, there may be a way to tension it, but in most cases, the belt is worn and needs replacement.

This is normal for a 210K Toyota Corolla. What you are hearing is the
sound made by the power steering pump. Check fluid level and fill as
needed. Some noise in the instances you are mentioning is normal.

You need to do a compression test on the engine cylinders. It appears one of the cylinders is not firing and dragging the rest of the engine down in power. The compression test will show if one of the cylinders has a problem.

My guess without hearing it, is that you have a loose or worn belt causing the screeching, or squeeling noise your hearing, but as far as sluggish goes, that may be another thing all together. I'd suggest having your belts looked at and adjusted or replaced as necessary. Once it's confirmed or not that your noise was from that or maybe even a tensioner, then we can go from there. In the meantime, chek your oil level just as a precaution, if you haven't lately, and top it up as needed. They are usually a pretty reliable car, so I wouldn't hit the panic button on it being an engine problem yet.